Question

the graph shows the cost, y, in dollars for a given number of pounds of yuca, x, that matias buys from the supermarket. what do the triangles tell you about the slope? complete each statement. the triangles are congruent. the ratios of the corresponding side lengths are the same. the slope of each part of the line is the same. which quotient shows how to use △abe to find the slope of the line? \\(\frac{be}{ae}\\) \\(\frac{ae}{be}\\) \\(\frac{ab}{ae}\\) \\(\frac{be}{ab}\\) slope = \\(\frac{\text{vertical change}}{\text{horizontal change}}\\) (graph: a(0,0), e(2,0), b(2,3), f(4,3), c(4,6), g(6,6), d(6,9) with x-axis 0–10 and y-axis 0–10)

Explanation:

Step1: Recall slope formula

Slope is defined as $\frac{\text{Vertical change}}{\text{Horizontal change}}$. For $\triangle ABE$, the vertical change is the length of $BE$ (change in $y$-axis) and the horizontal change is the length of $AE$ (change in $x$-axis).

Step2: Identify the quotient

So, the slope using $\triangle ABE$ is $\frac{BE}{AE}$.

Answer:

$\frac{BE}{AE}$ (corresponding to the first option: $\boldsymbol{\frac{BE}{AE}}$)